Efficient Publication of Sparse Data

ABSTRACT

The present disclosure is directed to systems, methods, and computer-readable storage media for publishing data. A data summary summarizing the data can be generated and published according to several publishing schemes. In some embodiments, non-zero entries are selected and modified and zero entries are sampled according to one or more distribution functions. The sampled and modified values are added to a data summary, or a sample of the sampled and modified values are added to the data summary. The data summary is published, released, used, or otherwise output. In other embodiments, priority values are assigned to each value associated with the data, and a number of entries with the highest values are selected and added to the data summary.

BACKGROUND

This application relates generally to publishing data. Morespecifically, the disclosure provided herein relates to efficientpublication of sparse data.

Many entities maintain or use data that includes sensitive informationabout clients, customers, users, and the like. These data can bevaluable to the entities, for example, the data can be analyzed todetermine usage patterns or trends, to identify and/or define audiencesand potential audiences, to identify business development or improvementopportunities, and/or for other purposes. These data also can bevaluable to the entities as a product that can be sold, leased, and/orotherwise shared with other entities for their own analysis, storage,and/or use.

One problem with using, storing, selling, or otherwise releasing thesedata is that the data often includes sensitive information. For example,entities sometimes store detailed demographic information aboutcustomers such as income information, shopping and purchasing histories,and the like. The data and associated sensitive information can includeenough detail that third parties are able to apply analysis and datamining techniques to determine identities of one or more customers andtheir associated demographic information. As such, privacy of customerscan be compromised by releasing data.

To address these and other concerns, various laws and regulations havebeen crafted to govern how data can be published or used withoutcompromising privacy or security of customers or other entities. Variousmethods are used to release the data in accordance with these laws andregulations, many of which require extensive consumption of resources.For example, some anonymization schemes used to enforce privacy onreleased data include adding noise to the values of the released data, aprocess that requires modification of a large number of valuesassociated with the data. For small data sets, these schemes arereasonable, but for large data sets these schemes can become undulyburdensome for the data owner and can make use or sharing of the dataimpracticable.

Furthermore, another challenge is faced when releasing or using sets orcollections of sparse data, i.e., data or data sets having a largeproportion, a majority, and/or a vast majority of zero-valued entries.For example, a data set of ten million commuters living and workingacross one million locations can result in a contingency table having1,000,000,000,000 entries, the vast majority of which will have valuesof “0.” Simply storing this data set would consume an enormous amount ofcomputing and/or storage resources, while adding noise to each entry orcell in this hypothetical contingency table would consume a dramaticallygreater amount of computing and storage resources, making such anapproach for protecting privacy unwieldy or even unmanageable.

SUMMARY

The present disclosure is directed to publication of data. In someembodiments, the data is sparse data that is efficiently published.According to various embodiments disclosed herein, the sparse data ispublished while maintaining differential privacy. In addition to thegenerally known definition of differential privacy, the phrase“differential privacy,” as used herein with respect to published data,refers to data that is published in accordance with a privacy approachthat maximizes accuracy of data and/or queries against the data whileminimizing the chances that one can identify one or more recordsassociated with the data. For example, published data complies with, orachieves, differential privacy if the probability of output falling insome set is at most exp(ε) times the probability of the output fallingin the same set, given input that differs in the records of at most oneindividual.

“Sparse data,” as used herein and in the claims, refers to data and/ordata sets having a large proportion, a majority, and/or a proportionexceeding a majority, of entries having values “0.” As used herein,“publishing” data includes, but is not limited to, outputting the data,publishing data or data sets, releasing data or data sets, sharing dataor data sets, anonymizing and/or summarizing data or data sets,formatting data or data sets in an analyzable format, combinationsthereof, and the like. In some embodiments, sparse data includes a vastmajority of zero-valued entries.

According to various embodiments disclosed herein, data is obtained. Thedata is obtained, in various implementations, by a summarization engine.A summary of the data (“data summary”) is generated using one or moresummarization and/or anonymization schemes. In some embodiments,non-zero entries are selected and modified and zero entries are sampledaccording to one or more distribution functions. The sampled andmodified values are added to a data summary, or a sample of the sampledand modified values are added to the data summary. The data summary ispublished, released, used, or otherwise output.

According to an aspect, a computer-implemented method for publishingdata includes obtaining data at a summarization engine. The dataobtained at the summarization engine can include two or more entries.The method also includes modifying one of the two or more of entries toobtain a resulting value, determining if the resulting value satisfies athreshold, and adding the resulting value to a data summary in responseto determining that the resulting value satisfies the threshold. Themethod also includes publishing the data summary.

In some embodiments, the one of the two or more entries includes one ofthe two or more entries that has a non-zero value. The method also caninclude sampling one or more zero-valued entries from the two or moreentries. Sampling the zero-valued entries can include sampling a numberof zero-valued entries. In some embodiments, the number of entries isdetermined according to a statistical distribution. For example, in someembodiments, the number of entries is determined according to a binomialdistribution. The sampled zero-valued entries are added to the datasummary and are associated with a noise value drawn from a statisticaldistribution. The method also can include adding the zero-valued entryto the data summary.

In some embodiments, modifying the one of the two or more entriesincludes adding noise to the one of the two or more entries. Modifyingthe one of the two or more entries also can include adding geometricnoise to the one of the two or more entries. In some implementations,the method further includes not adding the resulting value to the datasummary in response to determining that the resulting value does notsatisfy the threshold. The method also can include determining if thetwo or more entries includes a further non-zero entry, and selecting thefurther non-zero entry in response to determining that the two or moreentries includes the further non-zero entry. The data summary caninclude a data summary that is differentially private. In someembodiments, modifying the one of the two or more entries includesmodifying each non-zero valued entry of the two or more entries toobtain two or more resulting values. Adding the resulting value to thedata summary includes, in some instances, adding each of the two or moreresulting values that satisfies the threshold to the data summary.

According to another aspect, a computer-implemented method forpublishing data includes obtaining data at a summarization engine, thedata including two or more entries, and modifying one of the two or moreentries to obtain a resulting value. The one of the two or more valuesincludes a non-zero valued entry. The method also includes adding theresulting value to a data summary, sampling a number of zero-valuedentries from the two or more entries, adding the number of zero-valuedentries to the data summary, and publishing the data summary.

In some embodiments, sampling the number of zero-valued entries includesdetermining the number of zero-valued entries according to a statisticaldistribution such as a binomial distribution and sampling the determinednumber of zero-valued entries. Modifying the one of the two or moreentries can include adding noise to the one of the two or more entries.In some instances, the value of the noise added to the one of the two ormore entries is zero and in some instances the value of the noise is avalue other than zero. Modifying the one of the two or more entries alsocan include sampling the non-zero valued entry and adding the noise tothe non-zero valued entry. In some embodiments, the data summaryincludes a data summary that is differentially private.

According to another aspect, a computer-implemented method forpublishing data includes computer-implemented operations for obtainingdata at a summarization engine, the data including two or more entries.The method also includes assigning a priority value to each of the twoor more entries and drawing a sample from the two or more entries. Thesample can include two or more sampled entries. The method also includesadding the two or more sampled entries to a data summary, and publishingthe data summary.

In some embodiments, the method also includes identifying a sample size.A number of the two or more sampled entries can be equal to the samplesize. Drawing the sample can include selecting the two or more entriesby recursively removing from the two or more entries, and adding to thedata summary, an entry having a highest value. The data summaryincludes, in some embodiments, a data summary that is differentiallyprivate.

Other systems, methods, and/or computer program products according toembodiments will be or become apparent to one with skill in the art uponreview of the following drawings and detailed description. It isintended that all such additional systems, methods, and/or computerprogram products be included within this description, be within thescope of this disclosure, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a system diagram illustrating an illustrative system forefficient publication of sparse data, according to various embodimentsdisclosed herein.

FIG. 2 is a flow diagram showing aspects of a method for efficientpublication of sparse data, according to an illustrative embodiment.

FIG. 3 is a flow diagram showing aspects of a method for efficientpublication of sparse data, according to another illustrativeembodiment.

FIG. 4 is a flow diagram showing aspects of a method for efficientpublication of sparse data, according to yet another illustrativeembodiment.

FIG. 5 schematically illustrates a network, according to an illustrativeembodiment.

FIG. 6 is a block diagram illustrating an example computer systemconfigured to enable differentially private publication of sparse data,according to some illustrative embodiments.

DETAILED DESCRIPTION

The following detailed description is directed to methods, systems, andcomputer-readable media for efficient publication of sparse data. Whilethe subject matter described herein is presented in the general contextof program modules that execute in conjunction with the execution of anoperating system and application programs on a computer system, thoseskilled in the art will recognize that other implementations may beperformed in combination with other types of program modules. Generally,program modules include routines, programs, components, data structures,and other types of structures that perform particular tasks or implementparticular abstract data types. Moreover, those skilled in the art willappreciate that the subject matter described herein may be practicedwith other computer system configurations, including hand-held devices,multiprocessor systems, microprocessor-based or programmable consumerelectronics, minicomputers, mainframe computers, and the like.

Referring now to FIG. 1, aspects of a system 100 for efficientpublication of sparse data according to some illustrative embodimentspresented herein will be described. The system 100 shown in FIG. 1includes a data storage device 102. According to various embodiments,the functionality of the data storage device 102 described herein may beprovided by one or more server computers, databases, datastores,computer readable media (as defined herein), desktop computers, mobiletelephones, laptop computers, other computing systems, and the like. Thedata storage device 102 can be configured to operate on or incommunication with a network 104. An illustrative network 104 isdescribed in more detail below with reference to FIG. 5.

As illustrated in FIG. 1, the data storage device 102 stores or hostsone or more sets of data (“data”) 106. The data 106 can be stored inalmost any format including tables, contingency tables, matrices, textformats, tab- or other-character-delimited text formats, other formats,and the like. In some illustrative embodiments, the data 106 is storedin a database or data table. The data 106 can include any type of datathat may be useful for analysis or otherwise may be sold to, sharedwith, or released to various entities. Furthermore, the data 106described and illustrated herein corresponds to “sparse” data, asdefined herein. In many instances, a large proportion, e.g., eighty toninety percent or more of the values associated with the data 106 areequal to zero. In some embodiments, a vast majority, e.g., overninety-five percent, of entries in the data 106 are zero. It should beunderstood that these embodiments are illustrative, and should not beconstrued as being limiting in any way.

The data storage device 102 also can be configured to communicate with asummarization engine 108 via the network 104 and/or via a direct link.The summarization engine 108 is configured to execute an operatingsystem (not illustrated) and one or more application programs such as,for example, a summarization application 110, and/or other applicationprograms. The operating system is a computer program for controlling theoperation of the summarization engine 108.

The summarization application 110 is an executable program configured toexecute on top of the operating system to provide the functionalitydescribed herein for enabling differentially private publication of thedata 106. According to various implementations of the concepts andtechnologies disclosed herein, the summarization application 110 isconfigured to obtain the data 106, to apply noise and summarizationprocesses to the data 106 to generate a data summary 112, and topublish, release, share, and/or otherwise output the data summary 112.

In some embodiments, the summarization application 110 is configured togenerate the data summary 112 without actually applying noise to eachentry in the data 106 and/or without actually summarizing the data 106.As such, as explained herein in more detail, the summarizationapplication 110 is configured in some embodiments to generate the datasummary 112 from the data 106 using efficient processes for analyzing,selecting, adding noise to, sampling from, and/or summarizing the data106. According to various implementations of the concepts andtechnologies disclosed herein, the data summary 112 represents ananonymized summary of the data 106. The data summary 112 can consumeless data storage space than the data 106, can protect privacy ofvarious entities associated with the data 106, and can maintain theusefulness of the data 106.

In some embodiments, the summarization application 110 generates thedata summary 112 using a high-pass filter algorithm, as will bedescribed in more detail herein, particularly with reference to FIG. 2.According to some embodiments of the high-pass filter algorithm, thesummarization application 110 obtains the data 106 and selects anon-zero entry in the data 106. The summarization application 110 addsgeometric noise to the selected non-zero entry to obtain a resultingvalue. The summarization application 110 determines if the resultingvalue satisfies a defined threshold. If the resulting value satisfiesthe defined threshold, the resulting value is added to the data summary112. If the resulting value does not meet or exceed the definedthreshold, the resulting value is not added to the data summary 112. Thesummarization engine 108 can repeat these operations for each non-zeroentry in the data 106.

The summarization application 110 also is configured to add zero-valuedentries to the data summary 112. According to some embodiments, thesummarization application 110 samples a number k of values, wherein thenumber k is determined according to a statistical distribution. In someembodiments, the statistical distribution used to determine k is thebinomial distribution Bin(m−n, p_(θ)), where

$p_{\theta \overset{\Delta}{=}\frac{\alpha^{\theta}}{1 + \alpha}}.$

It should be understood that this embodiment is illustrative, and shouldnot be construed as being limiting in any way.

As used herein, m represents the total number of values or entries in aset of data 106, also represented herein as M, n represents the numberof non-zero values in m, θ is a threshold value determined or set by thesummarization application 110, Δ represents a sensitivity parameter, andα is defined as a function of a differential privacy parameter ε.Furthermore, according to various implementations, α is defined ase^(−ε/Δ). It should be understood that these embodiments areillustrative, and should not be construed as being limiting in any way.

According to various implementations of the concepts and technologiesdisclosed herein, the data 106, also denoted herein as M, can be sharedor released by a data owner. Prior to releasing M, however, the dataowner may need to take steps to protect entities associated with thedata 106. In some embodiments, noise is added to each value or entry inM, thereby obtaining a new data set having noise added to each value.This data set is denoted herein as M′. It should be noted that the noiseadded to each entry or value in M can be 0 or a non-zero value. The dataset M′ can be summarized by drawing a sample of values from M′, therebyallowing data owners and data users to store and use a representation ofthe data set M (referred to herein also as data 106). This summarizedversion of the data set M′ is denoted herein as M″ and/or the datasummary 112.

According to various implementations of the concepts and technologiesdisclosed herein, the summarization application 110 generates thesummarized version of the data M″, i.e., the data summary 112, withoutfirst generating the data set M′. In some embodiments, the summarizationapplication 110 further is configured to randomly select k locations ifrom the data 106 such that M(i)=0. For each of the k locations i, thesummarization application 110 includes i with value v in the datasummary 112 where v is sampled according to the distributionPr[X≦x]=(1=α^(x−θ+1)).

In other embodiments, the summarization application 110 generates thedata summary 112 using a threshold sampling algorithm, as will bedescribed in more detail herein, particularly with reference to FIG. 3.According to some embodiments of the threshold sampling algorithm, thesummarization application 110 obtains the data 106 and selects anon-zero entry in the data 106. The summarization application 110 addsgeometric noise to the non-zero entry to obtain a resulting value andadds the resulting value to the data summary according to a defineddistribution. According to some embodiments, the defined distribution is

${p_{i} = {\min \left( {\frac{{M^{\prime}(i)}}{\tau},1} \right)}},$

where τ is a sampling parameter determined or defined by thesummarization application 110. In some embodiments, the samplingparameter τ is greater than 0. The summarization engine 108 can repeatthese operations for each non-zero entry in the data 106.

The summarization application 110 also is configured to add zero-valuedentries to the data summary 112. According to some embodiments, thesummarization application 110 samples a number k of values, wherein thenumber k is determined according to a statistical distribution. In someembodiments, the statistical distribution is the binomial distributionBin((m−n),p_(τ)), where

$p_{\tau \overset{\Delta}{=}\frac{2{\alpha {({1 - \alpha^{\tau}})}}}{\tau {({1 - \alpha^{2}})}}}.$

It should be understood that this embodiment is illustrative, and shouldnot be construed as being limiting in any way. The summarizationapplication 110 further is configured to randomly select the k entries ifrom the data 106 such that M(i)=0. For each of the k entries, thesummarization application 110 draws the summary value M″(i) from thedistribution Pr [X≦v] given by

${{\tau\alpha}^{- v}{C_{\tau}\left( {1 - \alpha} \right)}},{{{if}\mspace{14mu} v} \leq {- \tau}},{C_{\tau}\left( {{{- v}\; \alpha^{- v}} + {\left( {v + 1} \right)\alpha^{{- v} + 1}} - \alpha^{\tau + 1}} \right)},{{{if}\mspace{14mu} - \tau} \leq v \leq 0},{{\frac{1}{2} +} \propto {C_{\tau}\left( {{1 - \left( {v + 1} \right)} \propto^{v}{+ v} \propto^{v + 1}} \right)}},{{{if}\mspace{14mu} 0} \leq v \leq \tau},{and}$${{\frac{1}{2} +} \propto {C_{\tau}\left( {{1 -} \propto^{\tau}{- \tau} \propto^{v}\left( {1 - \alpha} \right)} \right)}},{{{if}\mspace{14mu} v} > \tau},$

wherein C_(τ) is a constant that depends upon τ and α. According tovarious embodiments, C_(τ) is defined as

$\frac{1}{2{\alpha \left( {1 - \alpha^{\tau}} \right)}}.$

It should be understood that this embodiment is illustrative, and shouldnot be construed as being limiting in any way.

In yet other embodiments, including one illustrative embodimentillustrated in FIG. 4 below, the summarization application 110 generatesthe data summary 112 using a priority sampling scheme. According to someembodiments of the priority sampling scheme, the summarizationapplication 110 obtains the data 106 and assigns a priority to eachentry in the data 106, wherein the assigned priority is

${P_{i} = \frac{{M^{\prime}(i)}}{r_{i}}},$

where r_(i) is a random value chosen uniformly from the range (0,1). Thesummarization application 110 then draws a sample of size s by pickingthe items with the s largest priority values. In some embodiments, thesummarization application 110 is configured to retain the (s+1)thlargest priority value for estimation purposes.

FIG. 1 illustrates one data storage device 102, one network 104, and onesummarization engine 108. It should be understood, however, that variousimplementations of the system 100 include multiple data storage devices102, multiple networks 104, and multiple summarization engines 108.Therefore, the illustrated embodiment should be understood as beingillustrative, and should not be construed as being limiting in any way.

Turning now to FIG. 2, aspects of a method 200 for efficient publicationof sparse data will be described in detail, according to an illustrativeembodiment. It should be understood that the operations of the methodsdisclosed herein are not necessarily presented in any particular orderand that performance of some or all of the operations in an alternativeorder(s) is possible and is contemplated. The operations have beenpresented in the demonstrated order for ease of description andillustration. Operations may be added, omitted, and/or performedsimultaneously, without departing from the scope of the appended claims.

It also should be understood that the methods disclosed herein can beended at any time and need not be performed in its entirety. Some or alloperations of the methods, and/or substantially equivalent operations,can be performed by execution of computer-readable instructions includedon a computer storage media, as defined herein. The term“computer-readable instructions,” and variants thereof, as used in thedescription and claims, is used expansively hereinto include routines,applications, application modules, program modules, programs,components, data structures, algorithms, and the like. Computer-readableinstructions can be implemented on various system configurationsincluding single-processor or multiprocessor systems, minicomputers,mainframe computers, personal computers, hand-held computing devices,microprocessor-based, programmable consumer electronics, combinationsthereof, and the like.

Thus, it should be appreciated that the logical operations describedherein are implemented (1) as a sequence of computer implemented acts orprogram modules running on a computing system and/or (2) asinterconnected machine logic circuits or circuit modules within thecomputing system. The implementation is a matter of choice dependent onthe performance and other requirements of the computing system.Accordingly, the logical operations described herein are referred tovariously as states, operations, structural devices, acts, or modules.These states, operations, structural devices, acts, and modules may beimplemented in software, in firmware, in special purpose digital logic,and any combination thereof.

For purposes of illustrating and describing the concepts of the presentdisclosure, the method 200 is described as being performed by thesummarization engine 108. It should be understood that the summarizationengine 108, as well as additional and/or alternative devices and/ornetwork nodes, can provide the functionality described herein viaexecution of one or more application programs including, but not limitedto, the summarization application 110. Furthermore, it should beunderstood that the functionality of the summarization engine 108 can beprovided by any number of devices or network nodes, and is not limitedto the summarization engine 108 illustrated in the FIGURES. Thus, theillustrated embodiments are illustrative, and should not be viewed asbeing limiting in any way.

The method 200 begins at operation 202, wherein the summarization engine108 obtains the data 106. As explained above with reference to FIG. 1,the summarization engine 108 can obtain the data 106 from the datastorage device 102 in communication with the summarization engine 108and/or from other data storage locations. In some embodiments, the data106 is transmitted to the summarization engine 108, made available tothe summarization engine 108, and/or otherwise provided to thesummarization engine 108.

From operation 202, the method 200 proceeds to operation 204, whereinthe summarization engine 108 selects a non-zero entry in the data 106.Although not illustrated in FIG. 2, it should be understood that thesummarization engine 108 can be configured to analyze each entry in thedata 106 and to identify the non-zero entries. Thus, operation 204 caninclude identifying the non-zero entries in the data 106 and/orselecting one or more of the non-zero entries.

From operation 204, the method 200 proceeds to operation 206, whereinthe summarization engine 108 adds noise to the selected non-zero entry.As mentioned above, adding noise, also referred to herein and in theclaims as modifying the selected value, can include adding a value of 0to the selected value. Thus, someone observing the data with the noiseadded will be unaware of whether the value is the real value or thevalue with noise added. Thus, the operation 206 can include adding 0 tothe selected non-zero entry. According to some embodiments, thesummarization engine 108 adds geometric noise to the selected non-zeroentry according to one or more noise functions and/or according to oneor more random value generation functions. The non-zero entry with theadded geometric noise is referred to herein as a “resulting value.” Itshould be understood that the noise added to the selected non-zero entrycan have a negative value, and as such the resulting value can benegative. According to various implementations, negative values arerounded up to the nearest meaningful number, i.e., “0.” It should beunderstood that this embodiment is illustrative, and should not beconstrued as being limiting in any way.

From operation 206, the method 200 proceeds to operation 208, whereinthe summarization engine 108 determines if the resulting value obtainedin operation 206 satisfies a threshold. According to some embodiments,the threshold against which the resulting value is compared is selectedbased upon preferences, settings, values generated by one or moreapplied noise functions, combinations thereof, and the like. It can beappreciated that ideally the threshold is set such that “high” valuesare separated from “low values,” i.e., such that a large portion of thedata 106 does not pass the threshold comparison test, thereby shrinkingthe size of the data summary 112 relative to the size of the data 106.As such, the threshold value can be used to separate, via thedetermination in operation 208, the zero- or low-valued entries such aszero-valued entries having added noise values in the data 106, from thenon-zero entries.

If the summarization engine 108 determines in operation 208 that theresulting value satisfies the defined threshold, the method 200 proceedsto operation 210. At operation 210, the summarization engine 108 addsthe resulting value to the data summary 112. From operation 210, or fromoperation 208 if the summarization engine 108 determines that theresulting value does not satisfy the defined threshold, the method 200proceeds to operation 212.

At operation 212, the summarization engine 108 determines if the data106 includes another non-zero entry. If the summarization engine 108determines, in operation 212, that the data 106 includes anothernon-zero entry, the method 200 returns to operation 204, wherein thesummarization engine 108 selects another non-zero entry from the data106. The operations 204-212 can be repeated until all non-zero entriesin the data 106 have been processed by the summarization engine 108. Ifthe summarization engine 108 determines, in operation 212, that anothernon-zero entry does not exist in the data 106, the method 200 proceedsto operation 214.

At operation 214, the summarization engine 108 samples the zero-valuedentries in the data 106 and adds the sampled zero-valued entries to thedata summary 112. From operation 214, the method 200 proceeds tooperation 216, wherein the summarization engine 108 outputs the datasummary 112. As noted above, the data summary 112 output by thesummarization engine 108 can comply with the notion of differentialprivacy, but can be obtained without a two-step process of a) generatinga contingency table; and b) sampling from the generated contingencytable. Furthermore, as noted above, the word “output” as used hereinwith respect to outputting the data summary 112 includes, but is notlimited to, releasing the data summary 112, selling the data summary112, publishing the data summary 112, using the data summary 112, and/orotherwise making the data summary 112 available to one or more entities.As such, embodiments of the concepts and technologies disclosed hereinallow generation of the data summary 112 directly from the data 106,thereby obviating the need to perform resource-intensive summarizing andsampling operations that otherwise would be performed on the data 106.From operation 216, the method 200 proceeds to operation 218. The method200 ends at operation 218.

Turning now to FIG. 3, aspects of a method 300 for efficient publicationof sparse data will be described in detail, according to anotherillustrative embodiment. The method 300 begins at operation 302, whereinthe summarization engine 108 obtains the data 106. It should beunderstood that operation 302 can be substantially similar to operation202 described above. As such, the summarization engine 108 can obtainthe data 106 from the data storage device 102 or from other devices ornodes. As noted above, the data 106 can be transmitted to, madeavailable to, and/or otherwise provided to the summarization engine 108.

From operation 302, the method 300 proceeds to operation 304, whereinthe summarization engine 108 selects a non-zero entry from the data 106.As explained above with reference to operation 204, operation 304 caninclude identifying each non-zero entry in the data 106 and selection ofone of the identified non-zero entries. The non-zero entry selected inoperation 304 can be chosen at random and/or selected according to anydesired considerations. In some embodiments, for example, thesummarization engine 108 selects a first non-zero entry from the data106 by identifying the non-zero entry from the data 106 having a largestvalue or a smallest value, by selecting a first non-zero value in thedata 106, and/or according to other considerations. It should beunderstood that these embodiments are illustrative, and should not beconstrued as being limiting in any way.

From operation 304, the method 300 proceeds to operation 306, whereinthe summarization engine 108 adds noise to the selected non-zero entry.As mentioned above, adding noise, also referred to herein and in theclaims as modifying the selected value, can include adding a value of 0to the selected value. Thus, someone observing the data with the noiseadded will be unaware of whether the value is the real value or thevalue with noise added. Thus, the operation 306 can include adding 0 tothe selected non-zero entry. Again, the summarization engine 108 can addgeometric noise to the selected non-zero entry according to one or morefunctions. The non-zero entry with the added geometric noise is referredto herein as a “resulting value.” According to various implementations,the noise added to the selected non-zero entry is selected randomly ornon-randomly from a defined range.

From operation 306, the method 300 proceeds to operation 308, whereinthe summarization engine 108 adds the resulting value to the datasummary 112. According to various embodiments, the resulting value isadded to the data summary 112 with a defined probability. In oneembodiment, the probability with which the resulting value is added tothe data summary 112 is defined as

$p_{i} = {{\min \left( {\frac{{M^{\prime}(i)}}{\tau},1} \right)}.}$

It should be understood that this embodiment is illustrative, and shouldnot be construed as being limiting in any way.

From operation 308, the method 300 proceeds to operation 310, whereinthe summarization engine 108 determines if the data 106 includes anothernon-zero entry. If the summarization engine 108 determines, in operation308, that the data 106 includes another non-zero entry, the method 300returns to operation 304, wherein the summarization engine 108 selectsanother non-zero entry from the data 106. The operations 304-310 can berepeated until all non-zero entries in the data 106 have been processedby the summarization engine 108 or until the summarization engine 108proceeds for other reasons. If the summarization engine 108 determines,in operation 310, that another non-zero entry does not exist in the data106, the method 300 proceeds to operation 312.

At operation 312, the summarization engine 108 samples the zero-valuedentries in the data 106 and adds the sampled zero-valued entries to thedata summary 112. According to various embodiments, the samplingperformed by the summarization engine 108 in operation 312 includesuniformly and randomly selecting k entries i from the data 106 such thatthe probability with which the entries are selected satisfy a definedprobability. In one embodiment, the number k zero entries i are sampledfrom the data 106, and the value of k, i.e., the number of entriessampled from the data 106, is determined according to a statisticaldistribution. In some embodiments, the statistical distribution includesthe binomial distribution Bin((m−n),p_(τ)), where

$p_{\tau}\overset{\Delta}{=}{\frac{2{\alpha \left( {1 - \alpha^{\tau}} \right)}}{\tau \left( {1 - \alpha^{2}} \right)}.}$

It should be understood that this embodiment is illustrative, and shouldnot be construed as being limiting in any way.

From operation 312, the method 300 proceeds to operation 314, whereinthe summarization engine 108 outputs the data summary 112. As mentionedabove with reference to FIG. 1, the summarization engine 108 isconfigured to randomly select k entries i from the data 106, and to drawthe summary values as calculated in operations 302-312 from thedistribution Pr[X≦v] given by

${{\tau\alpha}^{- v}{C_{\tau}\left( {1 - \alpha} \right)}},{{{if}\mspace{14mu} v} \leq {- \tau}},{C_{\tau}\left( {{{- v}\; \alpha^{- v}} + {\left( {v + 1} \right)\alpha^{{- v} + 1}} - \alpha^{\tau + 1}} \right)},{{{if}\mspace{14mu} - \tau} \leq v \leq 0},{{\frac{1}{2} +} \propto {C_{\tau}\left( {{1 - \left( {v + 1} \right)} \propto^{v}{+ v} \propto^{v + 1}} \right)}},{{{if}\mspace{14mu} 0} \leq v \leq \tau},{and}$${{\frac{1}{2} +} \propto {C_{\tau}\left( {{1 -} \propto^{\tau}{- \tau} \propto^{v}\left( {1 - \alpha} \right)} \right)}},{{{if}\mspace{14mu} v} > {\tau.}}$

From operation 314, the method 300 proceeds to operation 316. The method300 ends at operation 316.

While not mentioned explicitly above, it should be understood thateither, both, or neither of the methods 200 and 300, noise can be addedto the sampled zero entries, as set forth at operations 214 and 312,respectively. Thus, the zero entries can be modified, if desired, in thesame manner as explained above with respect to the non-zero entriesprior to adding the zero entries to the data summary 112. It should beunderstood that this embodiment is illustrative, and should not beconstrued as being limiting in any way.

Turning now to FIG. 4, aspects of a method 400 for efficient publicationof sparse data will be described in detail, according to yet anotherillustrative embodiment. The method 400 begins at operation 402, whereinthe summarization engine 108 obtains the data 106. As explained abovewith reference to operations 202 and 302 of FIGS. 2 and 3, respectively,the summarization engine 108 can obtain the data 106 from the datastorage device 102 or from other devices or nodes, and that the data 106can be transmitted to, made available to, and/or otherwise provided tothe summarization engine 108.

From operation 402, the method 400 proceeds to operation 404, whereinthe summarization engine 108 assigns a priority value to each entry inthe data 106. In some embodiments, the assigned priority value isdefined as

${P_{i} = \frac{{M^{\prime}(i)}}{r_{i}}},$

where r_(i) is a random value chosen uniformly from the range (0,1). Itshould be understood that this embodiment is illustrative, and shouldnot be construed as being limiting in any way, as the priority valuescan be defined using other functions or relationships.

From operation 404, the method 400 proceeds to operation 406, whereinthe summarization engine 108 draws a sample from the data 106. Invarious implementations, the summarization engine 108 selects the samplebased, at least partially, upon the assigned priority values. The sampledrawn in operation 406 can be of size s. In some embodiments, thesummarization engine 108 selects the s items by identifying andselecting the entries in the data 106 having the s largest priorityvalues as assigned in operation 404. It should be understood that thisembodiment is illustrative, and should not be construed as beinglimiting in any way. According to another embodiment, the summarizationengine 108 also is configured to retain the (s+1) th largest priorityvalue for estimation purposes, though this is not necessarily the case.

From operation 406, the method 400 proceeds to operation 408, whereinthe summarization engine 108 outputs the data summary 112. It can beappreciated from the above description that the s entries having the slargest priority values can be added to the data summary 112, thoughthis step is not explicitly illustrated in FIG. 4. As such, operation408 includes outputting the s entries of the data 106 having the slargest priority values as assigned in operation 404. From operation408, the method 400 proceeds to operation 410. The method 400 ends atoperation 410.

Although not illustrated herein, some embodiments of the concepts andtechnologies disclosed herein include using a combination of samplingand filtering. In particular, in some embodiments, filtering is used toremove small counts from the data 106. This filtering is based upon anassumption that small counts result from the geometric noise added tozero-valued entries, and not from real inputs. Thus, the small counts inthe data 106 are assumed to be noise-based counts and therefore can beremoved. According to various embodiments of the concepts andtechnologies disclosed herein, if the threshold is set too low for thefiltering, some of the small counts resulting from the noise will beremoved, but many such counts may pass the filter. Similarly, if thethreshold is set too high, many real counts will be removed in additionto the noise-based counts.

In some embodiments, therefore, a combination of filtering and samplingis used. Thus, low frequency entries are filtered out of the data 106,and then a sample is drawn from the remaining entries in the data 106.In some embodiments, this filtering and sampling approach providesremoval of noise and bounded output size, thereby improving the resultsof the application.

Turning now to FIG. 5, additional details of the network 104 areillustrated, according to an illustrative embodiment. The network 104includes a cellular network 502, a packet data network 504, for example,the Internet, and a circuit switched network 506, for example, apublicly switched telephone network (“PSTN”). The cellular network 502includes various components such as, but not limited to, basetransceiver stations (“BTSs”), Node-B's or e-Node-B's, base stationcontrollers (“BSCs”), radio network controllers (“RNCs”), mobileswitching centers (“MSCs”), mobile management entities (“MMEs”), shortmessage service centers (“SMSCs”), multimedia messaging service centers(“MMSCs”), home location registers (“HLRs”), home subscriber servers(“HSSs”), visitor location registers (“VLRs”), charging platforms,billing platforms, voicemail platforms, GPRS core network components,location service nodes, an IP Multimedia Subsystem (“IMS”), and thelike. The cellular network 502 also includes radios and nodes forreceiving and transmitting voice, data, and combinations thereof to andfrom radio transceivers, networks, the packet data network 504, and thecircuit switched network 506.

A mobile communications device 508, such as, for example, a cellulartelephone, a user equipment, a mobile terminal, a PDA, a laptopcomputer, a handheld computer, and combinations thereof, can beoperatively connected to the cellular network 502. The cellular network502 can be configured as a 2G GSM network and can provide datacommunications via GPRS and/or EDGE. Additionally, or alternatively, thecellular network 502 can be configured as a 3G UMTS network and canprovide data communications via the HSPA protocol family, for example,HSDPA, EUL (also referred to as HSUPA), and HSPA+. The cellular network502 also is compatible with 4G mobile communications standards as wellas evolved and future mobile standards.

The packet data network 504 includes various devices, for example,servers, computers, databases, and other devices in communication withanother, as is generally known. The packet data network 504 devices areaccessible via one or more network links. The servers often storevarious files that are provided to a requesting device such as, forexample, a computer, a terminal, a smartphone, or the like. Typically,the requesting device includes software (a “browser”) for executing aweb page in a format readable by the browser or other software. Otherfiles and/or data may be accessible via “links” in the retrieved files,as is generally known. In some embodiments, the packet data network 504includes or is in communication with the Internet. The circuit switchednetwork 506 includes various hardware and software for providing circuitswitched communications. The circuit switched network 506 may include,or may be, what is often referred to as a plain old telephone system(POTS). The functionality of a circuit switched network 506 or othercircuit-switched network are generally known and will not be describedherein in detail.

The illustrated cellular network 502 is shown in communication with thepacket data network 504 and a circuit switched network 506, though itshould be appreciated that this is not necessarily the case. One or moreInternet-capable devices 510, for example, a PC, a laptop, a portabledevice, or another suitable device, can communicate with one or morecellular networks 502, and devices connected thereto, through the packetdata network 504. It also should be appreciated that theInternet-capable device 510 can communicate with the packet data network504 through the circuit switched network 506, the cellular network 502,and/or via other networks (not illustrated).

As illustrated, a communications device 512, for example, a telephone,facsimile machine, modem, computer, or the like, can be in communicationwith the circuit switched network 506, and therethrough to the packetdata network 504 and/or the cellular network 502. It should beappreciated that the communications device 512 can be anInternet-capable device, and can be substantially similar to theInternet-capable device 510. In the specification, the network 104 isused to refer broadly to any combination of the networks 502, 504, 506.It should be appreciated that substantially all of the functionalitydescribed with reference to the network 104 can be performed by thecellular network 502, the packet data network 504, and/or the circuitswitched network 506, alone or in combination with other networks,network elements, and the like.

FIG. 6 is a block diagram illustrating a computer system 600 configuredto verify transactions using user devices, in accordance with variousembodiments of the concepts and technologies disclosed herein. Thecomputer system 600 includes a processing unit 602, a memory 604, one ormore user interface devices 606, one or more input/output (“I/O”)devices 608, and one or more network devices 610, each of which isoperatively connected to a system bus 612. The bus 612 enablesbi-directional communication between the processing unit 602, the memory604, the user interface devices 606, the I/O devices 608, and thenetwork devices 610.

The processing unit 602 may be a standard central processor thatperforms arithmetic and logical operations, a more specific purposeprogrammable logic controller (“PLC”), a programmable gate array, orother type of processor known to those skilled in the art and suitablefor controlling the operation of the server computer. Processing unitsare generally know, and therefore are not described in further detailherein.

The memory 604 communicates with the processing unit 602 via the systembus 612. In some embodiments, the memory 604 is operatively connected toa memory controller (not shown) that enables communication with theprocessing unit 602 via the system bus 612. The memory 604 includes anoperating system 614 and one or more program modules 616. The operatingsystem 614 can include, but is not limited to, members of the WINDOWS,WINDOWS CE, and/or WINDOWS MOBILE families of operating systems fromMICROSOFT CORPORATION, the LINUX family of operating systems, theSYMBIAN family of operating systems from SYMBIAN LIMITED, the BREWfamily of operating systems from QUALCOMM CORPORATION, the MAC OS, iOS,and/or LEOPARD families of operating systems from APPLE CORPORATION, theFREEBSD family of operating systems, the SOLARIS family of operatingsystems from ORACLE CORPORATION, other operating systems, and the like.The program modules 616 may further include the summarizationapplication 110. In some embodiments, the summarization application 110is embodied in computer-readable media containing instructions that,when executed by the processing unit 602, perform one or more of themethods 200, 300, 400 for efficient publication of sparse data, asdescribed in detail above with respect to FIGS. 2-4. According toembodiments, the program modules 616 may be embodied in hardware,software, firmware, or any combination thereof.

By way of example, and not limitation, computer-readable media mayinclude any available computer storage media or communication media thatcan be accessed by the computer system 600. Communication media includescomputer-readable instructions, data structures, program modules, orother data in a modulated data signal such as a carrier wave or othertransport mechanism and includes any delivery media. The term “modulateddata signal” means a signal that has one or more of its characteristicschanged or set in a manner as to encode information in the signal. Byway of example, and not limitation, communication media includes wiredmedia such as a wired network or direct-wired connection, and wirelessmedia such as acoustic, RF, infrared and other wireless media.Combinations of the any of the above should also be included within thescope of computer-readable media.

Computer storage media includes volatile and non-volatile, removable andnon-removable media implemented in any method or technology for storageof information such as computer-readable instructions, data structures,program modules, or other data. Computer storage media includes, but isnot limited to, RAM, ROM, Erasable Programmable ROM (“EPROM”),Electrically Erasable Programmable ROM (“EEPROM”), flash memory or othersolid state memory technology, CD-ROM, digital versatile disks (“DVD”),or other optical storage, magnetic cassettes, magnetic tape, magneticdisk storage or other magnetic storage devices, or any other mediumwhich can be used to store the desired information and which can beaccessed by the computer system 600. In the claims, the phrase “computerstorage medium” and variations thereof, does not include waves, signals,and/or other transitory and/or intangible communication media, per se.

The user interface devices 606 may include one or more devices withwhich a user accesses the computer system 600. The user interfacedevices 606 may include, but are not limited to, computers, servers,personal digital assistants, cellular phones, or any suitable computingdevices. The I/O devices 608 enable a user to interface with the programmodules 616. In one embodiment, the I/O devices 608 are operativelyconnected to an I/O controller (not shown) that enables communicationwith the processing unit 602 via the system bus 612. The I/O devices 608may include one or more input devices, such as, but not limited to, akeyboard, a mouse, or an electronic stylus. Further, the I/O devices 608may include one or more output devices, such as, but not limited to, adisplay screen or a printer.

The network devices 610 enable the computer system 600 to communicatewith other networks or remote systems via a network, such as the network104. Examples of the network devices 610 include, but are not limitedto, a modem, a radio frequency (“RF”) or infrared (“IR”) transceiver, atelephonic interface, a bridge, a router, or a network card. The network104 may include a wireless network such as, but not limited to, aWireless Local Area Network (“WLAN”) such as a WI-FI network, a WirelessWide Area Network (“WWAN”), a Wireless Personal Area Network (“WPAN”)such as BLUETOOTH, a Wireless Metropolitan Area Network (“WMAN”) such aWiMAX network, or a cellular network. Alternatively, the network 108 maybe a wired network such as, but not limited to, a Wide Area Network(“WAN”) such as the Internet, a Local Area Network (“LAN”) such as theEthernet, a wired Personal Area Network (“PAN”), or a wired MetropolitanArea Network (“MAN”).

Based on the foregoing, it should be appreciated that systems andmethods for efficient publication of sparse data have been disclosedherein. Although the subject matter presented herein has been describedin language specific to computer structural features, methodological andtransformative acts, specific computing machinery, and computer-readablemedia, it is to be understood that the invention defined in the appendedclaims is not necessarily limited to the specific features, acts, ormedia described herein. Rather, the specific features, acts and mediumsare disclosed as example forms of implementing the claims.

The subject matter described above is provided by way of illustrationonly and should not be construed as limiting. Various modifications andchanges may be made to the subject matter described herein withoutfollowing the example embodiments and applications illustrated anddescribed, and without departing from the true spirit and scope of theembodiments, which is set forth in the following claims.

1. A computer-implemented method for publishing data, the methodcomprising computer-implemented operations at least for: obtaining dataat a summarization engine, the data comprising a plurality of entries;modifying one of the plurality of entries to obtain a resulting value;determining if the resulting value satisfies a threshold; in response todetermining that the resulting value satisfies the threshold, adding theresulting value to a data summary; and publishing the data summary. 2.The method of claim 1, wherein the one of the plurality of the entriescomprises one of the plurality of entries having a non-zero value. 3.The method of claim 2, further comprising sampling a zero-valued entryfrom the plurality of entries.
 4. The method of claim 3, whereinsampling the zero-valued entry comprises sampling a number ofzero-valued entries, the number of zero-valued entries comprising thezero-valued entry, wherein the number is determined according to astatistical distribution, and wherein sampling the zero-valued entryfurther comprises adding the sampled zero-valued entry to the datasummary.
 5. The method of claim 4, further comprising adding thezero-valued entry to the data summary.
 6. The method of claim 2, whereinmodifying the one of the plurality of entries comprises adding noise tothe one of the plurality of entries.
 7. The method of claim 1 whereinmodifying the one of the plurality of entries comprises adding a valueof zero to the one of the plurality of entries.
 8. The method of claim1, further comprising not adding the resulting value to the data summaryin response to determining that the resulting value does not satisfy thethreshold.
 9. The method of claim 2, further comprising determining ifthe plurality of entries comprises a further non-zero entry; andselecting the further non-zero entry in response to determining that theplurality of entries comprises the further non-zero entry.
 10. Themethod of claim 1, wherein the data summary comprises a data summarythat is differentially private.
 11. The method of claim 1, whereinmodifying the one of the plurality of entries comprises modifying eachnon-zero valued entry of the plurality of entries to obtain a pluralityof resulting values, and wherein adding the resulting value to the datasummary comprises adding each of the plurality of resulting values thatsatisfies the threshold to the data summary.
 12. A computer-implementedmethod for publishing data, the method comprising computer-implementedoperations at least for: obtaining data at a summarization engine, thedata comprising a plurality of entries; modifying one of the pluralityof entries to obtain a resulting value, the one of the plurality ofvalues comprising a non-zero valued entry; adding the resulting value toa data summary; sampling a zero-valued entry from the plurality ofentries; adding the zero-valued entry to the data summary; andpublishing the data summary.
 13. The method of claim 12, whereinsampling the zero-valued entry comprises sampling a number ofzero-valued entries, the number of zero-valued entries comprising thezero-valued entry, and wherein the number is determined according to astatistical distribution.
 14. The method of claim 12, wherein modifyingthe one of the plurality of entries comprises adding noise to the one ofthe plurality of entries.
 15. The method of claim 13, wherein modifyingthe one of the plurality of entries comprises sampling the non-zerovalued entry and adding the noise to the non-zero valued entry.
 16. Themethod of claim 12, wherein the data summary comprises a data summarythat is differentially private.
 17. A computer-implemented method forpublishing data, the method comprising computer-implemented operationsat least for: obtaining data at a summarization engine, the datacomprising a plurality of entries; assigning a priority value to each ofthe plurality of entries; drawing a sample from the plurality ofentries, the sample comprising a plurality of sampled entries; addingthe plurality of sampled entries to a data summary; and publishing thedata summary.
 18. The method of claim 17, further comprising identifyinga sample size, wherein a number of the plurality of sampled entries isequal to the sample size.
 19. The method of claim 18, wherein drawingthe sample comprises selecting the plurality of entries by recursivelyremoving from the plurality of entries, and adding to the data summary,an entry having a highest value.
 20. The method of claim 17, wherein thedata summary comprises a data summary that is differentially private.